Encoding and decoding data arrays using separate pre-multiplication stages

ABSTRACT

Some embodiments of the invention provide a method of performing a Discrete Cosine Transform (“DCT”) encoding or decoding coefficients of a data array by (1) multiplying the coefficients by a scalar value before the encoding or decoding, and then (2) dividing the encoded or decoded coefficients by the scalar value. When used in conjunction with fixed-point arithmetic, this method increases the precision of the encoded and decoded results. In addition, some embodiments provide a method of performing a two-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). This method splits a pre-multiplication operation of the iDCT into two or more separate stages. When used in conjunction with fixed-point arithmetic, this splitting increases the precision of the decoded results of the iDCT.

RELATED APPLICATIONS

This patent application claims the benefit under title 35, United StatesCode, Section 119(e) to the U.S. Provisional Patent Application entitled“Method and Apparatus for Coding and Decoding,” having Ser. No.60/396,156 filed on Jul. 14, 2002.

FIELD OF THE INVENTION

The present invention is directed towards encoding and decoding dataarrays using separate pre-multiplication stages.

BACKGROUND OF THE INVENTION

Moving Picture Experts Group (MPEG) video compression is currently usedin many video products such as digital television set-top boxes, DSS,HDTV decoders, DVD players, video conferencing, Internet video, andother applications. These products benefit from MPEG video compressionsince compressed video requires less storage space for video informationand less bandwidth for the transmission of the video information.

An MPEG video is a sequence of video frames comprised of intra codedI-frames and/or inter coded P and B-frames, as is well known in the art.Each video frame is typically divided into sub-sections of macro blocks(16×16 pixels in a data array). A macro block typically includessub-sections of four luminance blocks and two chrominance blocks (8×8data arrays). A luminance block specifies brightness information (e.g.,luminance image coefficients) about the pixels in the block, while thetwo chrominance blocks specify Cr and Cb color information (e.g., Cr andCb image coefficients) about the pixels in the macro block.

MPEG video encoding and decoding processes typically use discrete cosinetransform (“DCT”) and inverse DCT (“iDCT”) to encode and decodecoefficients of a block (i.e., data array). A DCT operation takes imagevalues defined in a spatial domain and transforms them into a frequencydomain. The DCT operation transforms the inputted image values into alinear combination of weighted basis functions. These basis functionsare the frequency components of the inputted image values. As such, whena DCT operation is applied to a block of image values, it yields a blockof weighted values corresponding to how much of each basis function ispresent in the original image to be encoded.

For most images, most of the image information lies at low frequencieswhich appear in the upper-left corner of the DCT-encoded block. Thelower-right values of the DCT-encoded block represent higherfrequencies, and are often small enough to be neglected with littlevisible distortion. The top left corner value in the DCT-encoded blockis the DC (zero-frequency) component and lower and rightmore entriesrepresent larger vertical and horizontal spatial frequencies.

The DCT operation is a separable transform in that the matrix thatdefines this transformation is decomposable into two matrices, one thatcorresponds to a column transform and another that corresponds to a rowtransform. Thus it can be implemented as two one-dimensional (1D)transforms. In other words, a two-dimensional (2D) DCT is just a 1D DCTapplied twice, once in the column direction and once in the rowdirection. In the case of a 1D 8-point DCT, the first coefficient (theDC coefficient) represents the average value of the image values and theeighth coefficient represents the highest frequencies found in theimage. An iDCT operation is used to convert the frequency coefficientsback into the image information.

DCT encoding of a block is a two-dimensional (2D) transformationoperation that can be expressed by the following formula:

${F\left( {u,v} \right)} = {\frac{C_{u}}{2}\frac{C_{v}}{2}{\sum\limits_{y = 0}^{7}\; {\sum\limits_{x = 0}^{7}\; {{f\left( {x,y} \right)}{\cos\left\lbrack \frac{\left( {{2x} + 1} \right)u\; \pi}{16} \right\rbrack}{\cos\left\lbrack \frac{\left( {{2y} + 1} \right)v\; \pi}{16} \right\rbrack}}}}}$with: $C_{u} = \left\{ {\begin{matrix}\frac{1}{\sqrt{2}} & {{{{if}\mspace{14mu} n} = 0},} \\1 & {{{if}\mspace{14mu} u} > 0}\end{matrix};{C_{v} = \left\{ \begin{matrix}\frac{1}{\sqrt{2}} & {{{{if}\mspace{14mu} v} = 0},} \\1 & {{{if}\mspace{14mu} v} > 0}\end{matrix} \right.}} \right.$

In the formula above, a column dimension of the block is represented byx values and a row dimension of the block is represented by y values, sothat f(x,y) is the image information at position [x,y] of the block. Assuch, F(u,v) is the 2D encoded image information at position [u,v] ofthe 2D encoded block.

A DCT decoder performs an inverse DCT transformation on a DCT encodedblock to reconstruct the block. DCT decoding of a block is also atwo-dimensional (2D) transformation operation, which can be expressed bythe following formula:

${f\left( {x,y} \right)} = {\sum\limits_{u = 0}^{7}\; {\sum\limits_{v = 0}^{7}\; {{F\left( {u,v} \right)}\frac{C_{u}}{2}\frac{C_{v}}{2}{\cos\left\lbrack \frac{\left( {{2x} + 1} \right)u\; \pi}{16} \right\rbrack}{\cos\left\lbrack \frac{\left( {{2y} + 1} \right)v\; \pi}{16} \right\rbrack}}}}$

In the formula above, the columns of the 2D encoded block arerepresented by u values and the rows of the 2D encoded block arerepresented by v values, so that F(u,v) is the encoded image data atposition [u,v] of the block. As such, f(x,y) is the image data atposition [x,y] of the block.

Conventionally, 2D DCT and 2D iDCT processes contain a pre-multiplystage that multiplies each coefficient of the block to be transformed bya pre-multiplication value. The pre-multiplication value is usually lessthan one. As such, the pre-multiplication operation results in the lossof precision, when it is used in conjunction with fixed point arithmeticthat rounds or truncates the multiplication results.

SUMMARY OF THE INVENTION

Some embodiments of the invention provide a method of performing aDiscrete Cosine Transform (“DCT”) encoding or decoding coefficients of adata array by (1) multiplying the coefficients by a scalar value beforethe encoding or decoding, and then (2) dividing the encoded or decodedcoefficients by the scalar value. When used in conjunction withfixed-point arithmetic, this method increases the precision of theencoded and decoded results.

In addition, some embodiments provide a method of performing atwo-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). Thismethod splits a pre-multiplication operation of the iDCT into two ormore separate stages. When used in conjunction with fixed-pointarithmetic, this splitting increases the precision of the decodedresults of the iDCT.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth in the appendedclaims. However, for purpose of explanation, several embodiments of theinvention are set forth in the following figures.

FIG. 1 illustrates a process that performs a 2D iDCT operation.

FIG. 2 illustrates a process that performs a 2D DCT operation.

FIG. 3 illustrates a process that receives a DCT-encoded data stream,generates a DCT-encoded block, and decodes the block using only onetranspose operation.

FIG. 4 illustrates a process that DCT encodes a data array and outputsthe DCT-encoded data array using only one transpose operation.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, numerous details are set forth for purposeof explanation. However, one of ordinary skill in the art will realizethat the invention may be practiced without the use of these specificdetails. In other instances, well-known structures and devices are shownin block diagram form in order not to obscure the description of theinvention with unnecessary detail.

Some embodiments of the invention provide a method of performing aDiscrete Cosine Transform (“DCT”) encoding or decoding of coefficientsof a data array by (1) multiplying the coefficients by a scalar valuebefore the encoding or decoding, and then (2) dividing the encoded ordecoded coefficients by the scalar value. When used in conjunction withfixed-point arithmetic, this method increases the precision of theencoded and decoded results.

In addition, some embodiments provide a method of performing atwo-dimensional (2D) Inverse Discrete Cosine Transform (“iDCT”). Thismethod splits a pre-multiplication operation of the iDCT into two ormore separate stages. When used in conjunction with fixed-pointarithmetic, this splitting increases the precision of the decodedresults of the iDCT.

Several embodiments are described below by reference to FIGS. 1 to 4.These embodiments are part of an MPEG encoder or decoder that encodes ordecodes video frames by using 2D DCT and IDCT operations on 8-by-8 imageblocks (i.e., data arrays). One of ordinary skill, however, will realizethat other embodiments might use other compression techniques (e.g.,H.263 compression). Alternatively, other embodiments might use othertypes of transformations (such as those used in MPEG 4 part 10). Also,other embodiments might apply their transform operations on differentsize blocks, such as 4×4, 8×4, or any n×m set of pixels, where n and mare integers.

DCT decoding is a separable two-dimensional (2D) transform operation.The separable nature of the iDCT decoding can be exploited by (1)performing a first 1D iDCT process in the column direction of the 2Dencoded block to produce a ID encoded block and then a second 1D iDCTprocess in the row direction of the encoded block to produce the block.Alternatively, the first 1D iDCT operation can be performed in the rowdirection of the 2D encoded block and the second 1D iDCT operation canbe performed in the column direction of the encoded block.

The scaled-version of the Chen method can be used to perform two ID iDCToperations. This scaled-version is described in the paper “2D InverseDiscrete Cosine Transform,” which can be found athttp://e-www.motorola.com, incorporated herein by reference. The Chenalgorithm is an efficient implementation of the iDCT operation thatrequires a fewer number of computations than a straightforwardimplementation of the iDCT.

FIG. 1 illustrates a process 100 that performs a 2D iDCT operation. Thisprocess decodes a data array of coefficients that were encoded using aDCT operation. As shown in FIG. 1, the process 100 initially multiplies(at 105) each coefficient in the data array by a scalar value S. In someembodiments, the scalar value is 16. These embodiments perform themultiplication by shifting up each coefficient in the data array by fourbits. Some of these embodiments shift up each coefficient by four bitssince (1) in these embodiments, each coefficient in the data array canbe represented by a 12 bit value, and (2) these embodiments perform16×16 fixed point multiplication. A 16×16 fixed point multiplicationmultiplies two 16 bit values to obtain a 32 bit value, which it thenconverts into a 16 bit value by truncating the lowest 16 bits androunding the 17th bit (which after the truncation will be the 1^(st)bit) based on the truncated 16 bits.

After 105, the process performs (at 110) a first pre-multiplicationoperation for a first 1D iDCT operation. In some embodiments, the firstpre-multiplication operation entails multiplying each coefficient of thedata array that remains after 105 by a value of a followingpre-multiplication array (A):

c4 c1 c2 c3 c4 c3 c2 c1 (A) c4 c1 c2 c3 c4 c3 c2 c1 c4 c1 c2 c3 c4 c3 c2c1 c4 c1 c2 c3 c4 c3 c2 c1 c4 c1 c2 c3 c4 c3 c2 c1 c4 c1 c2 c3 c4 c3 c2c1 c4 c1 c2 c3 c4 c3 c2 c1 c4 c1 c2 c3 c4 c3 c2 c1where cN=cos(Nπ/16).

Next, the process performs (at 115) a first 1D iDCT operation. In someembodiments, the process performs the first 1D iDCT operation accordingto the scaled-version of the Chen method, which is described in theabove-referenced paper. The first 1D iDCT operation is either along therow direction or the column direction. In the embodiments describedbelow, the first 1D iDCT operation is along the column direction.

After 115, the process performs (at 120) a second pre-multiplicationoperation for a second 1D iDCT operation. In some embodiments, thesecond pre-multiplication operation entails multiplying each coefficientof the data array that remains after 105 by a value of a followingpre-multiplication array (A):

Next, the process performs (at 125) a second 1D iDCT operation. Like thefirst 1D iDCT operation, the process performs the second 1D iDCToperation according to the scaled-version of the Chen method, which isdescribed in the above-referenced paper. The second 1D iDCT operationcan also be either along the row direction or the column direction. Inthe embodiments described below, the second 1D iDCT operation is alongthe row direction.

From 125, the process transitions to 130. At 130, the process divides byfour each coefficient in the data array that remains after 125. Thisdivision is part of the iDCT pre-multiplication operation, which theprocess 100 divides into three stages 110, 120, and 130. By splittingthe pre-multiplication operation into separate stages, the processmaintains larger coefficient values that result in less precision losswhen fixed-point multiplication is used.

After 130, the process divides (at 135) each coefficient by the scalarvalue S that it used as the multiplier at 105. When the scalar value is16, the division at 135 entails shifting down each coefficient by fourbits. Although 130 and 135 are illustrated as two separate operations inFIG. 1, one of ordinary skill will realize that both operations can beperformed simultaneously. For instance, when the scalar value is 16, theprocess can perform 130 and 135 by shifting down each coefficient by sixbits.

Like iDCT decoding, DCT encoding is a separable two-dimensional (2D)transform operation. The separable nature of the DCT encoding operationcan be exploited by (1) performing a first one-dimensional (1D) DCToperation in the column direction of the image block to produce a 1Dencoded block, and then (2) performing a second 1D DCT operation in therow direction of the 1D encoded block to produce a 2D encoded block.Alternatively, the first 1D DCT operation can be performed in the rowdirection of the block and the second 1D DCT operation performed in thecolumn direction of the block.

The scaled-version of the Chen method can be used to perform the two 1DDCT operations. This scaled-version is described in the paper “2DDiscrete Cosine Transform,” which can be found athttp://e-www.motorola.com, incorporated herein by reference. The Chenalgorithm is an efficient implementation of the DCT operation thatrequires a fewer number of computations than a straightforwardimplementation of the DCT. While a straightforward implementation of theDCT requires a number of computations that is proportional to N̂2 (whereN=8 for an 8-point DCT), the Chen algorithm exploits symmetry andperiodicity inherent in the DCT calculation to reduce the number ofcomputations to an amount proportional to N log(N).

FIG. 2 illustrates a process 200 that performs a 2D DCT operation. Thisprocess encodes a data array of coefficients. As shown in FIG. 2, theprocess 200 initially multiplies (at 205) each coefficient in the dataarray by a scalar value S. Some embodiments use a scalar value of 16,and hence perform the multiplication by shifting up each coefficient inthe data array by four bits. Some of these embodiments shift eachcoefficient of by four bits for the reason described above for someembodiments of FIG. 1.

After 205, the process performs (at 210) a first 1D DCT operation. Insome embodiments, the process performs the first 1D DCT operationaccording to the scaled-version of the Chen method, which is describedin the second paper referenced above. The first 1D DCT operation iseither along the row direction or the column direction. In theembodiments described below, the first 1D DCT operation is along thecolumn direction.

After 210, the process performs (at 215) a second 1D DCT operation. Likethe first 1D DCT operation, the process performs the second 1D DCToperation according to the scaled-version of the Chen method, which isdescribed in the second paper referenced above. The second 1D DCToperation can also be either along the row direction or the columndirection. In the embodiments described below, the second 1D DCToperation is along the row direction.

Next, at 220, the process performs a post multiply operation, accordingto the scaled-version of the Chen method. After 220, the process divides(at 225) each coefficient by the scalar value S that it used as themultiplier at 205. When the scalar value is 16, the division at 225entails shifting down each coefficient by four bits. Although 220 and225 are illustrated as two separate operations in FIG. 2, one ofordinary skill will realize that both operations can be performedsimultaneously.

When 2D DCT encoding and decoding processes are separated into two 1DDCT operations or two 1D iDCT operations, transpose operations aretypically performed between the 1D operations. Conventionally, twotranspose operations are used in each of the encoding and decodingprocesses. One approach uses only one transpose operation in each of theencoding and decoding processes, as disclosed in U.S. Patent Applicationentitled “Video Encoding and Decoding,” Attorney Docket No. APLE.P0021,Express Mail Label No. EV 117694264 US, filed concurrently herewith,,which is incorporated herein by reference.

FIG. 3 illustrates a process 300 that receives a DCT-encoded datastream, generates a DCT-encoded block, and decodes the block using onlyone transpose operation. The operations of the process 300 are similarto the operations of the process 100 of FIG. 1. Hence, similar numbersare used to described similar operations in these figures.

The process 300 starts when it receives a data stream of encoded values.The process 300 parses out and derasterizes (at 305) the values of thedata stream and stores the values in a data array according to atransposed zig-zag scan order. The transposed zig-zag scan order isidentical to a conventional zig-zag scan order except that it has beenflipped symmetrically about the diagonal line that connects the top-leftand the bottom-right corners of the data array. The process thenperforms (at 310) an inverse quantization process on the data array. Foran MPEG encoding, the inverse quantization entails multiplying eachvalue of the data array by a value of a transposed quantization matrix.The transposed quantization matrix is a transposed version of thequantization matrix used by conventional MPEG inverse quantizers.

The process 300 then multiplies (at 105) each coefficient in the dataarray by a scalar value S. The process performs (at 110) a firstpre-multiplication operation for a first 1D iDCT operation. Next, theprocess performs (at 115) a first 1D iDCT operation. The first 1D iDCToperation is either along the row direction or the column direction. Inthe embodiments described below, the first 1D iDCT operation is alongthe column direction.

The process next performs (at 315) a transpose operation on thecoefficients of the data array that exists after 115. A transposeoperation interchanges the row and columns of an array. In other words,a transpose A^(T) of an array A is an array that is symmetricallyrelated to the array A, such that row i in A^(T) is column j in A, andcolumn j in A^(T) is row i in A.

The process then performs (at 120) a second pre-multiplication operationfor a second 1D iDCT operation. Next, the process performs (at 125) asecond 1D iDCT operation. The second 1D iDCT operation can also beeither along the row direction or the column direction. In theembodiments described below, the second 1D iDCT operation is along therow direction. The process then divides (at 130) by four eachcoefficient in the data array that remains after 125. The process thendivides (at 135) each coefficient by the scalar value S that it used asthe multiplier at 105. The process then ends.

FIG. 4 illustrates a process 400 that DCT encodes a data array ofcoefficients and outputs the DCT-encoded data array using only onetranspose operation. The operations of the process 400 are similar tothe operations of the process 200 of FIG. 2. Hence, similar numbers areused to described similar operations in these figures.

As shown in FIG. 4, the process 400 initially multiplies (at 205) eachcoefficient in the data array by a scalar value S. The process thenperforms (at 210) a first 1D DCT operation. The first 1D DCT operationis either along the row direction or the column direction. In theembodiments described below, the first 1D DCT operation is along thecolumn direction.

The process next performs (at 405) a transpose operation on thecoefficients of the data array that exists after 210. The processperforms (at 215) a second 1D DCT operation. The second 1ID DCToperation can also be either along the row direction or the columndirection. In the embodiments described below, the second 1D DCToperation is along the row direction. Next, at 220, the process performsa post multiply operation, according to the scaled-version of the Chenmethod. After 220, the process divides (at 225) each coefficient by thescalar value S that it used as the multiplier at 205.

The process then performs (at 407) a quantization operation. For an MPEGencoding, the quantization entails multiplying each value of the dataarray (that exists after 225) by a value of a transposed quantizationmatrix. The process then rasterizes (at 410) the coefficients of thedata array remaining after 407 in a transposed zig-zag scan order toproduce a data stream. The process then ends.

While the invention has been described with reference to numerousspecific details, one of ordinary skill in the art will recognize thatthe invention can be embodied in other specific forms without departingfrom the spirit of the invention. Several embodiments described aboverelate to MPEG compression. One of ordinary skill in the art, however,will realize that the invention can relate to other types ofcompression, such as H.263 compression. However, if other compressiontechniques are used, some of the aspects of the above-describedprocesses might have to be modified.

1. (canceled)
 2. A method for decoding a data array of coefficients thathas been encoded according to a two-dimensional (2D) transform encodingoperation that is separable in to two one-dimensional (1D) transformoperations, the method comprising: multiplying each coefficient in thedata array by a first pre-multiplication value; performing a first 1Dinverse transform on the data array resulting from the multiplying;multiplying each coefficient in the data array resulting from the first1D inverse transform by a second pre-multiplication value; andperforming a second 1D inverse transform on the data array resultingfrom the multiplying by the second pre-multiplication value.
 3. Themethod of claim 2 further comprising: dividing each coefficient in thedata array resulting from the second 1D inverse transform by four. 4.(canceled)
 5. (Canceled)
 6. A method for decoding a data stream ofvalues that has been encoded according to a two-dimensional (2D)transform encoding operation that is separable in to two one-dimensional(1D) transform operations, the method comprising: parsing encoded valuesout of the data stream and creating a two-dimensional data array thatstores the encoded values in a particular scan order, wherein the valuesin the created data array are encoded in both dimensions of the array;multiplying each value in the data array by a first pre-multiplicationvalue; performing a first 1D inverse transform on the data arrayresulting from the multiplying; transposing the data array resultingfrom the first 1D inverse transform; multiplying each value in the dataarray resulting from the transposing by a second pre-multiplicationvalue; and performing a second 1D inverse transform on the data arrayresulting from the multiplying by the second pre-multiplication value.7. The method of claim 6 further comprising: dividing each value in thedata array resulting from the second 1D inverse transform by four. 8.The method of claim 6, wherein the particular scan order is a transposedzig-zag scan order. 9-12. (canceled)